Jarvis Cocker joined David Bowie, Peter Ustinov and David Attenborough on the list of narrators of the Prokofiev children's classic. Photograph: Felix Clay for the Guardian

Being asked to narrate Peter and the Wolf is like being cast as Lear: the ultimate sign you have pricked a certain layer of the nation's consciousness. David Bowie has done it. So has Peter Ustinov. Ditto Patrick Stewart, Ben Kingsley and David Attenborough. It was only a matter of time, then, before Jarvis Cocker was given the honour.

Like those that have gone before him, the Pulp singer is the owner of a voice you'd recognise underwater, a deep and warm tenor with vowels as flat as his native Sheffield is hilly.

"Hello everyone. I'm Jarvis," he said with a salute, as he strode on to the stage at London's Royal Festival Hall. The introduction was not superfluous. While Cocker will be remembered by anyone over 30 after his bottom sabotaged Michael Jackson's performance at the Brit awards in 1996, to most of today's audience he was just a messy-haired man wearing a lot of brown – the kind of dishevelled chap you used to see on BBC2 if you got up too early and watched the Open University.

Many of those in the auditorium were still at nursery when Michael Jackson died – and not even alive when the OU went off air back in 2006. Five-year-old Bella had been told by her uncle, Andrew Clark, that they were going to see the singer in one of his favourite bands. But she was more interested in the animal noises. "I like the cat," she said. "It's played by the castanets. I mean, the clarinet. I'm always getting those mixed up." What's the name of the man telling the story, asked Uncle Andrew. "Umm," said Bella. "I've forgotten."

Before he began, Cocker explained we were going to hear Prokofiev's work twice. "You are getting the Brucie bonus," he said to an audience far too young for the reference. "The first time I'll be reading the story, and the second time you will be watching an award-winning film." Both versions would be accompanied by the Philharmonia Orchestra, he said. "The first time you'll have to make the pictures in your head, and then you can compare them to the ones on screen." Then he introduced the animals: the fluttering flute to represent the bird; the waddle and quiver of the oboe as the duck; the French horns for the big bad wolf, the timpani for the hunters and the jaunty strings playing Peter. "And which instrument is the grandfather?" Cocker asked the crowd. "The bassoon!" chorused a choir of small voices, some of whom had attended the pre-show workshop in which animateur Luke Crookes provided a masterclass in Prokofiev's kiddie classic.

As the story unfolded, tiny voices could be heard whispering: "Mum! Is that the hunters?" and "Dad, I think I can hear the wolf." The jumpier members of the audience flinched when Cocker, as Peter, yelled "Look out!" when the bird was about to be pounced on by the cat. He was a fantastic narrator: deadpan, but never boring. Some people put on baby voices to read to young crowds, but Cocker sounded just the same as he did singing Babies back in 1992.

Perhaps inevitably, though, he was upstaged by the film that followed him. In these celluloid days when kids watch a DVD in the back on every car journey, pictures will always win out over audio alone. Especially when the film is as delightful as Suzie Templeton's animated version, which won the best animation Oscar in 2008. Children and grown-ups roared as the duck skated on the ice, gasped as Peter lassoed the wolf and giggled as a flightless bird strapped a balloon on its back in an attempt to fly. But Cocker didn't mind. Sitting cross-legged on stage, he seemed as enthralled as everyone else.